It's been possible to pay for sex in the real world since there was something to trade. It's not called "the oldest profession" for no reason. It's possible right now, and it will, most likely, always be possible. It's also a thing that exists in 2020, although I'm sure (I can't remember off the cuff) the rulebook/corebooks do not go into detail regarding it, as far as pricing and so on goes. Still, 2020 is an RPG, and rules only exist as a tool.
As such, the world of 2077 would most likely, obviously, have prostitution. Now, should the PC/console game have it, and should the player be able to partake in it...well, the question is why not. Why shouldn't there be prostitution, and why shouldn't it be available to the player. If the answer to that question is that prostitution is somehow a "bad thing", then we're getting into a political discussion about something that not all people are opposed to, at all. Quite a few people, myself included, think that people should be free to sell sex, if that's what they want to do. Sex-slavery and the worst forms of pimping (abuse, threats, extortion and so on), of course, are something that comes with the territory, and should be fought against.
Still, it's a thing that exists. I see no legitimate reason existing to make the decision not to have it in the game. Having said that, there should be a fitting reason to have it, and it should be made so that it fits the lore of Night City.